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Nonequilibrium steady states (NESSs) in periodically driven dissipativequantum systems are vital in Floquet engineering. We develop a general theoryfor high-frequency drives with Lindblad-type dissipation to characterize andanalyze NESSs based on the high-frequency (HF) expansion with linear algebraicnumerics and without numerically solving the time evolution. This theory showsthat NESSs can deviate from the Floquet-Gibbs state depending on thedissipation type. We show the validity and usefulness of the HF-expansionapproach in concrete models for a diamond nitrogen-vacancy (NV) center, akicked open XY spin chain with topological phase transition under boundarydissipation, and the Heisenberg spin chain in a circularly-polarized magneticfield under bulk dissipation. In particular, for the isotropic Heisenbergchain, we propose the dissipation-assisted terahertz (THz) inverse Faradayeffect in quantum magnets. Our theoretical framework applies to varioustime-periodic Lindblad equations that are currently under active research.

Nonequilibrium steady states in the Floquet-Lindblad systems: van Vleck's high-frequency expansion approach